如图,在△ABC中,AB=AC,D、E分别在BC、AC上,且AD=AE,若∠BAD=20°,则∠CDE=_.
问题描述:
如图,在△ABC中,AB=AC,D、E分别在BC、AC上,且AD=AE,若∠BAD=20°,则∠CDE=______.
答
设∠DAC=x°,
∵AB=AC,
∴∠B=
=(80−180°−(20+x)° 2
)°,x 2
∴∠ADC=20°+(80−
)°=(100-x 2
)°,x 2
∵AD=AE,
∴∠ADE=
=(90-180°−x° 2
)°,x 2
∴∠CDE=(100-
)°-(90-x 2
)°=10°,x 2
故答案为:10°.